Chapter 1.3, Problem 114E

(a)

To determine

To explain the reason due to which the median and the IQR is considered a better choice to summarize the data.

Explanation of Solution

Given:

The output:

  

  

As it can be clearly seen in the given box plot that the dataset is positively skewed, and when the data is skewed the median is considered as the best measure to summarize the data. This is because the median and interquartile range is resistant to the extreme values and the outliers while mean and standard deviation are not resistant to extreme value or outliers because all the values are being taken into the account while calculating the mean and standard deviation due to which even if the one value has been changed from the dataset then the value of mean and standard deviation changes.

(b)

To determine

To explain the things that is being shown in stem and leaf diagram which is not being shown in box plot.

Explanation of Solution

Dot plot shows all the all values of the dataset on the graph while the box plot shows the five number summaries on the graph. It can clearly observe the number of values that falls at particular place or less than particular value. Also, it is easier to know the shape of the distribution in dot plot because all the value are clearly visible while in box plot it is require to compare the boxes, median, Q1 and Q3.